Thinly slice the cucumber, green pepper, onions and radishes. Cut the avocado into 1/2-inch cubes. Place all vegetables, including the cabbage in a salad bowl, and chill in the refrigerator for 30 minutes.

In a small bowl, mix together the vinegar, lime juice, salt, pepper, and, if desired, the sugar. Whisk in the olive oil until the dressing is completely blended.

Pour the dressing over the salad, and thoroughly combine the ingredients. Divide the salad among six plates, and serve.